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Open AccessArticle

On Multidimensional Congestion Games

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Department of Mathematics and Physics “Ennio De Giorgi”, University of Salento-Provinciale Lecce-Arnesano, P.O. Box 193, 73100 Lecce, Italy
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Gran Sasso Science Institute-Viale Francesco Crispi 7, 67100 L’Aquila, Italy
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Department of Information Engineering Computer Science and Mathematics, University of L’Aquila-Via Vetoio, Loc. Coppito, 67100 L’Aquila, Italy
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Authors to whom correspondence should be addressed.
This work widely improves on an extended abstract presented at SIROCCO 2012.
Algorithms 2020, 13(10), 261; https://doi.org/10.3390/a13100261
Received: 9 September 2020 / Revised: 27 September 2020 / Accepted: 3 October 2020 / Published: 15 October 2020
(This article belongs to the Special Issue Graph Algorithms and Applications)
We introduce multidimensional congestion games, that is, congestion games whose set of players is partitioned into d+1 clusters C0,C1,,Cd. Players in C0 have full information about all the other participants in the game, while players in Ci, for any 1id, have full information only about the members of C0Ci and are unaware of all the others. This model has at least two interesting applications: (i) it is a special case of graphical congestion games induced by an undirected social knowledge graph with independence number equal to d, and (ii) it represents scenarios in which players have a type and the level of competition they experience on a resource depends on their type and on the types of the other players using it. We focus on the case in which the cost function associated with each resource is affine and bound the price of anarchy and stability as a function of d with respect to two meaningful social cost functions and for both weighted and unweighted players. We also provide refined bounds for the special case of d=2 in presence of unweighted players. View Full-Text
Keywords: congestion games; pure Nash equilibrium; potential games; price of anarchy; price of stability congestion games; pure Nash equilibrium; potential games; price of anarchy; price of stability
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Bilò, V.; Flammini, M.; Gallotti, V.; Vinci, C. On Multidimensional Congestion Games. Algorithms 2020, 13, 261.

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